## Abstract and Applied Analysis

### On the Mean Values of Certain Character Sums

#### Abstract

Let $q\ge \mathrm{5}$ be an odd number. In this paper, we study the fourth power mean of certain character sums ${\sum }_{\chi \text{mod}q,\left(\chi -1\right)=-1}^{\mathrm{*}}{\left|{\sum }_{1\le a\le q/4}a\chi \left(a\right)\right|}^{4}$ and ${\sum }_{\chi \text{mod}q,\left(\chi -1\right)=1}^{\mathrm{*}}{\left|{\sum }_{1\le a\le q/4}a\chi \left(a\right)\right|}^{4}$, where ${{\sum \mathrm{‍}}^{\mathrm{*}}}_{}$ denotes the summation over primitive characters modulo $q$, and give some asymptotic formulae.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 326597, 19 pages.

Dates
First available in Project Euclid: 27 February 2014

https://projecteuclid.org/euclid.aaa/1393512170

Digital Object Identifier
doi:10.1155/2013/326597

Mathematical Reviews number (MathSciNet)
MR3134154

Zentralblatt MATH identifier
1303.11093

#### Citation

Xu, Zhefeng; Liu, Huaning. On the Mean Values of Certain Character Sums. Abstr. Appl. Anal. 2013 (2013), Article ID 326597, 19 pages. doi:10.1155/2013/326597. https://projecteuclid.org/euclid.aaa/1393512170

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